36over 25 rays to power 3over 2 whole rays to power5over3
I can not decipher your text
right off for example
(36/25)^(3/2)
or
[36/(25)^3]/2
or what, no hope unless you use parentheses properly
the "rays" instead of "raised" doesn't help any. I read it as
((36/25)^(3/2)) ^ (5/3)
due to the sly "whole" meaning "all that has come before".
Now, since
36 = 6^2, 36^(3/2) = 6^3
25 = 5^2, 25^(3/2) = 5^3
Now, raise those to the 5/3 power, and you wind up with
6^5/5^5 = 7776/3125
Of course, almost any other interpretation might be as valid.
To simplify the expression (36/25)^(3/2) * (36/25)^(5/3), we can follow these steps:
Step 1: Simplify each term separately
First, let's simplify (36/25)^(3/2):
To simplify a fractional exponent, we can rewrite it using the concept of a radical. The exponent in this case, 3/2, suggests taking the cube root of the base raised to the power of 3. So, we have:
(36/25)^(3/2) = ∛(36/25)^3
Now, we can simplify the numerator and denominator separately:
36^3 = 36 * 36 * 36 = 46656
25^3 = 25 * 25 * 25 = 15625
Substituting these values back, we get:
(36/25)^(3/2) = ∛(46656/15625)
Now, let's simplify (36/25)^(5/3):
Again, we can rewrite the exponent as a radical:
(36/25)^(5/3) = ∛(36/25)^5
Simplifying the numerator and denominator:
36^5 = 36 * 36 * 36 * 36 * 36 = 60466176
25^5 = 25 * 25 * 25 * 25 * 25 = 9765625
Substituting these values back into the equation:
(36/25)^(5/3) = ∛(60466176/9765625)
Step 2: Combine the two simplified terms
Now, we can combine the simplified terms:
(∛(46656/15625)) * (∛(60466176/9765625))
Simplifying further, we can multiply the two radicals:
∛((46656 * 60466176)/(15625 * 9765625))
Calculating the numerator and denominator:
46656 * 60466176 = 2821109907456
15625 * 9765625 = 152587890625
The expression becomes:
∛(2821109907456/152587890625)
Step 3: Evaluate the cube root
Finally, we evaluate the cube root of the fraction:
∛(2821109907456/152587890625) ≈ 1.531
Therefore, the simplified expression is approximately equal to 1.531.